my homework lesson 5 divide by 4

Curriculum  /  Math  /  5th Grade  /  Unit 2: Multiplication and Division of Whole Numbers  /  Lesson 5

Multiplication and Division of Whole Numbers

Lesson 5 of 20

Criteria for Success

Tips for teachers, anchor tasks.

Problem Set

Target Task

Additional practice.

Multiply two-digit, three-digit, and four-digit numbers by one-digit numbers.

Common Core Standards

Core standards.

The core standards covered in this lesson

Number and Operations in Base Ten

5.NBT.B.5 — Fluently multiply multi-digit whole numbers using the standard algorithm.

Foundational Standards

The foundational standards covered in this lesson

4.NBT.B.4 — Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.A.2 — Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Compute two-digit, three-digit, and four-digit by one-digit products using the area model, the partial products algorithm, and the standard algorithm. 
• Relate the area model, the partial products algorithm, and the standard algorithm. 
• Round to estimate two-digit, three-digit, and four-digit by one-digit products.

Suggestions for teachers to help them teach this lesson

• Students multiplied up to four-digit by one-digit whole numbers using the area model, the partial products algorithm, and/or the standard algorithm in Grade 4. The intention of this lesson it to review these strategies, and particularly the standard algorithm, with these cases before moving on to multiplication with larger factors in later lessons. 
• Throughout this topic, it is important to preserve place value when talking about products of multi-digit numbers. For example, when discussing the computation  $$1,768\times4$$ , the partial product of the 6 digit and the 4 digit should be referenced as “six tens times four” or “sixty times four” rather than “six times four.”

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Here is one way to find the area of a rectangle that is 43 units by 2 units. 

You might be familiar with different ways to write multiplication calculations. Here are two ways to calculate 43  $$\times$$  2. 

Calculation A                     Calculation B

a.   In Calculation A, how are each of the partial products obtained? For instance, where does the 6 come from?

b.   In Calculation B, how is 86 obtained?

c.   Look at the area model. How are the partial products in Calculation A and the 86 in Calculation B related to the numbers in the area model?

Guiding Questions

Grade 6, Unit 5, Lesson 7, Teacher Version is made available by Open Up Resources  under the  CC BY 4.0  license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Dec. 7, 2018, 11:15 a.m..

a.   Find the value of $$932\times4$$ .

b.   Swathi used the standard algorithm to find the value of $$932\times4$$ . Here is her work.

• Where do you see $$2\times4$$  in Swathi's work?
• What does the 1 on the equal line represent in Swathi's calculation? Where did it come from?
• Where did the digits 3 and 7 in the solution come from?

Grade 5 Unit 4 Lesson 6 Activity 1 “Compose a New Unit” is made available by Open Up Resources  under the  CC BY 4.0  license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Sept. 15, 2021, 11:49 a.m..

Estimate the following products. Then solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help.

a.    $$4,408\times5$$

b.    $$5,731\times7$$

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

• Look at #4. Can the expression 8 x (3,000 + 600 + 5) be used to find the value of 3,605 x 8? Why or why not? What other expressions can be used to solve 3,605 x 8? How do you know? 
• Look at #5. What is an example of when Nina’s claim is true? What is an example of when Nina’s claim is not true? 
• What was the value of the question mark in #6? How did you figure that out? 
• Look at #7. What is a possible number that Casey multiplies 178 by? Is there more than one right answer? 

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve. Show or explain your work.

a.   42 × 3 

b.   6 × 215

c.   2,039 × 8

Student Response

Grade 4 Mathematics > Module 3 > Mid-Module Assessment of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds . © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US  license. Accessed Dec. 22, 2017, 1:59 p.m..

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Topic A: Writing and Interpreting Numerical Expressions

Evaluate numerical expressions involving addition, subtraction, multiplication, division, and grouping symbols.

Write expressions that record calculations with numbers, and interpret expressions without evaluating them.

5.OA.A.1 5.OA.A.2

Write expressions that represent real-world situations and evaluate them.

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Topic B: Multi-Digit Whole Number Multiplication

Multiply multiples of powers of ten. Estimate multi-digit products by rounding numbers to their largest place value. 

Multiply two-digit numbers by two-digit numbers.

Multiply three-digit numbers by two-digit numbers.

Multiply four-digit numbers by two-digit numbers.

Multiply three- and four-digit numbers by three-digit numbers.

Multiply multi-digit numbers and assess the reasonableness of the product.

Topic C: Multi-Digit Whole Number Division

Divide multiples of powers of ten by multiples of ten without remainders. Estimate multi-digit quotients by rounding numbers to their largest place value.

Estimate multi-digit quotients using compatible numbers.

Divide two-digit, three-digit, and four-digit dividends by one-digit divisors.

Divide two- and three-digit dividends by multiples of 10 with one-digit quotients and remainders in the ones place.

Divide two-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.

Divide three-digit dividends by two-digit divisors with one-digit quotients and remainders in the ones place.

Divide three-digit dividends by two-digit divisors with two-digit quotients, reasoning about the decomposition of a remainder in any place.

Divide four-digit dividends by two-digit divisors with two- and three-digit quotients, reasoning about the decomposition of a remainder in any place.

Divide multi-digit numbers by one- and two-digit divisors and assess the reasonableness of the quotient.

Solve word problems involving multi-digit multiplication and division.

5.NBT.B.5 5.NBT.B.6 5.OA.A.1 5.OA.A.2

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Unit 5: Division

About this unit.

• Division: FAQ (Opens a modal)
• Estimating division that results in non-whole numbers (Opens a modal)
• Understanding remainders (Opens a modal)
• Introduction to remainders (Opens a modal)
• Interpreting remainders (Opens a modal)
• Estimate to divide by 1-digit numbers Get 3 of 4 questions to level up!
• Interpret remainders Get 3 of 4 questions to level up!
• Divide with remainders (2-digit by 1-digit) Get 3 of 4 questions to level up!

Divide multiples of 10, 100, and 1,000 by 1-digit numbers

• Quotients that are multiples of 10 (Opens a modal)
• Divide multiples of 10, 100, and 1,000 by 1-digit numbers Get 5 of 7 questions to level up!

Division with place value

• Division using place value (Opens a modal)
• Divide using place value Get 3 of 4 questions to level up!

Division with area models

• Division with area models (Opens a modal)
• Create division equations with area models Get 3 of 4 questions to level up!
• Divide by 1-digit numbers with area models Get 3 of 4 questions to level up!

Estimate quotients

• Estimating quotients (Opens a modal)
• Estimate quotients (3- and 4-digit divided by 1-digit) Get 3 of 4 questions to level up!

Multi-digit division with partial quotients

• Introduction to division with partial quotients (no remainder) (Opens a modal)
• Division with partial quotients (remainder) (Opens a modal)
• Intro to long division (no remainders) (Opens a modal)
• Divide multi-digit numbers by 2, 3, 4, and 5 (remainders) Get 5 of 7 questions to level up!
• Divide multi-digit numbers by 6, 7, 8, and 9 (remainders) Get 3 of 4 questions to level up!

Multiplication, division word problems

• Division word problem: field goals (Opens a modal)
• Multiplication word problem: pizza (Opens a modal)
• Multiplication and division word problems Get 5 of 7 questions to level up!

Multi-step word problems

• 2-step estimation word problem (Opens a modal)
• 2-step estimation word problems Get 3 of 4 questions to level up!
• Represent multi-step word problems using equations Get 3 of 4 questions to level up!
• Multi-step word problems with whole numbers Get 3 of 4 questions to level up!

Common Core Grade 5 Math (Worksheets, Homework, Lesson Plans)

Looking for video lessons that will help you in your Common Core Grade 5 Math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Grade 5 students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. The Lesson Plans and Worksheets are divided into six modules.

Related Pages Common Core Math Resources, Lesson Plans And Worksheets Common Core Math Video Lessons, Math Worksheets and Games for Grade 5 Common Core Math Video Lessons, Math Worksheets and Games for all grades

Grade 5 Homework, Lesson Plans And Worksheets

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Eureka Math Grade 5 Module 4 Lesson 29 Answer Key

Engage ny eureka math 5th grade module 4 lesson 29 answer key, eureka math grade 5 module 4 lesson 29 problem set answer key.

Question 1. Divide. Rewrite each expression as a division sentence with a fraction divisor, and fill in the blanks. The first one is done for you.

Example: 2 ÷ 0.1 = 2 ÷ \(\frac{1}{10}\) = 20 There are 10 tenths in 1 whole. There are 20 tenths in 2 wholes.

a. 5 ÷ 0.1 There are ____ tenths in 1 whole. There are ____ tenths in 5 wholes.

Answer: There are 10 tenths in 1 whole. There are 50 tenths in 5 wholes.

Explanation: Given that 5 ÷ 0.1 which is 50. In that, there are 10 tenths in 1 whole and there are 50 tenths in 5 wholes.

There are ____ tenths in 1 whole. There are ____ tenths in 8 wholes.

Answer: There are 10 tenths in 1 whole. There are 8 tenths in 5 wholes.

Explanation: Given that 8 ÷ 0.1 which is 80. In that, there are 10 tenths in 1 whole and there are 80 tenths in 8 wholes.

c. 5.2 ÷ 0.1

There are tenths in 5 wholes. There are ____ tenths in 2 tenths. There are ____ tenths in 5.2.

Answer: There are 2 tenths in 2 tenths. There are 52 tenths in 5.2.

d. 8.7 ÷ 0.1 There are ____ tenths in 8 wholes. There are ____ tenths in 7 tenths. There are ____ tenths in 8.7.

Answer: There are 80 tenths in 8 wholes. There are 7 tenths in 7 tenths. There are 87 tenths in 8.7.

Explanation: Given that 8.7 ÷ 0.1 which is 87. In that, there are 80 tenths in 8 whole and there are 7 tenths in 7 tenths and there are 87 tenths in 8.7.

e. 5 ÷ 0.01 There are 100 hundredths in 1 whole. There are 500 hundredths in 5 wholes.

Answer: There are ____ hundredths in 1 whole. There are ____ hundredths in 5 wholes.

Explanation: Given that 5 ÷ 0.01 which is 500. In that, there are 100 hundredths in 1 whole and there are 500 hundredths in 5 wholes.

f. 8 ÷ 0.01 There are ____ hundredths in 1 whole. There are ____ hundredths in 8 wholes.

Answer: There are 100 hundredths in 1 whole. There are 800 hundredths in 8 wholes.

Explanation: Given that 8 ÷ 0.01 which is 800. In that, there are 100 hundredths in 1 whole and there are 800 hundredths in 8 wholes.

g. 5.2 ÷ 0.01 There are ____ hundredths in 5 wholes. There are ____ hundredths in 2 tenths. There are ____ hundredths in 5.2.

Answer: There are 500 hundredths in 1 whole. There are 20 hundredths in 5 tenths. There are 520 hundredths in 5.2.

Explanation: Given that 5.2 ÷ 0.01 which is 520. In that, there are 500 hundredths in 1 whole and there are 20 hundredths in 5 tenths and there are 520 hundredths in 5.2.

h. 8.7 ÷ 0.01 There are ____ hundredths in 8 wholes. There are ____ hundredths in 7 tenths. There are ____ hundredths in 8.7.

Answer: There are 800 hundredths in 8 whole. There are 70 hundredths in 7 tenths. There are 870 hundredths in 8.7.

Explanation: Given that 8.7 ÷ 0.01 which is 870. In that, there are 800 hundredths in 8 whole and there are 70 hundredths in 7 tenths and there are 870 hundredths in 8.7.

Question 2. Divide. a. 6 ÷ 0.1

Answer: 6 ÷ 0.1 = 60.

Explanation: The division of 6 ÷ 0.1 is 60.

b. 18 ÷ 0.1

Answer: 18 ÷ 0.1 = 180.

Explanation: The division of 18 ÷ 0.1 is 180.

c. 6 ÷ 0.01

Answer: 6 ÷ 0.01 = 600.

Explanation: The division of 6 ÷ 0.01 is 600.

d. 1.7 ÷ 0.1

Answer: 1.7 ÷ 0.1 = 17.

Explanation: The division of 1.7 ÷ 0.1 is 17.

e. 31 ÷ 0.01

Answer: 31 ÷ 0.01 = 3,100.

Explanation: The division of 31 ÷ 0.01 is 3,100.

f. 11 ÷ 0.01

Answer: 11 ÷ 0.01 = 1,100.

Explanation: The division of 11 ÷ 0.01 is 1,100.

g. 125 ÷ 0.1

Answer: 125 ÷ 0.1 = 1,250.

Explanation: The division of 125 ÷ 0.1 is 1,250.

h. 3.74 ÷ 0.01

Answer: 3.74 ÷ 0.01 = 374.

Explanation: The division of 3.74 ÷ 0.01 is 374.

i. 12.5 ÷ 0.01

Answer: 12.5 ÷ 0.01 = 1,250.

Explanation: The division of 12.5 ÷ 0.01 is 1,250.

Question 3. Yung bought $4.60 worth of bubble gum. Each piece of gum cost $0.10. How many pieces of bubble gum did Yung buy?

Answer: Yung bought 46 pieces of gum.

Explanation: Here, Yung bought $4.60 worth of bubble gum, and each piece of gum cost $0.10. So the number of pieces of bubble gum did Yung bought is $4.60 ÷ $0.10 = $46. So Yung bought 46 pieces of gum.

Question 4. Cheryl solved a problem: 84 ÷ 0.01 = 8,400. Jane said, “Your answer is wrong because when you divide, the quotient is always smaller than the whole amount you start with, for example, 6 ÷ 2 = 3 and 100 ÷ 4 = 25.” Who is correct? Explain your thinking.

Answer: Some examples are, 84 ÷ 1 = 84, 84 ÷ 10 = 8.4, 84 ÷ 0.1 = 840.

Explanation: Cheryl is correct and Jane is correct only some of the time and Cheryl can help Jane understand by showing some examples like, 84 ÷ 1 = 84, 84 ÷ 10 = 8.4, 84 ÷ 0.1 = 840.

Question 5. The U.S. Mint sells 2 ounces of American Eagle gold coins to a collector. Each coin weighs one-tenth of an ounce. How many gold coins were sold to the collector? Answer: The number of gold coins was sold to the collector is 20 gold coins.

Explanation: Here, U.S. Mint sells 2 ounces of American Eagle gold coins to a collector and each coin weighs one-tenth of an ounce, so the number of gold coins were sold to the collector is 2 ÷ 1/10 which is 2 ÷ 0.1 = 20 gold coins.

Eureka Math Grade 5 Module 4 Lesson 29 Exit Ticket Answer Key

Question 1. 8.3 is equal to _______ tenths _______ hundredths Answer: 83 tenths 830 hundredths.

Explanation: Given that the number is 8.3 which is equal to 83 tenths and 830 hundred.

Question 2. 28 is equal to _______ hundredths _______ tenths Answer: 2800 tenths 830 hundredths.

Question 3. 15.09 ÷ 0.01 = _______ Answer: 15.09 ÷ 0.01 = 1,509.

Explanation: Given that the equation is 15.09 ÷ 0.01 which is equal to 1,509.

Question 4. 267.4 ÷ \(\frac{1}{10}\) = _______ Answer: 267.4 ÷ \(\frac{1}{10}\) = 2,674

Explanation: Given that the equation is 267.4 ÷ \(\frac{1}{10}\) which is equal to 2,674.

Question 5. 632.98 ÷ \(\frac{1}{100}\) = _______ Answer: 632.98 ÷ \(\frac{1}{100}\) = 63,298

Explanation: Given that the equation is 632.98 ÷ \(\frac{1}{100}\) which is equal to 63,298.

Eureka Math Grade 5 Module 4 Lesson 29 Homework Answer Key

Question 1. Divide. Rewrite each expression as a division sentence with a fraction divisor, and fill in the blanks. The first one is done for you. a. 9 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 9 wholes.

Answer: There are 10 tenths in 1 whole. There are 90 tenths in 9 wholes.

Explanation: Given that 9 ÷ 0.1 which is 90. In that, there are 10 tenths in 1 whole and there are 90 tenths in 9 wholes.

b. 6 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 6 wholes.

Answer: There are 10 tenths in 1 whole. There are 60 tenths in 6 wholes.

Explanation: Given that 6 ÷ 0.1 which is 60. In that, there are 10 tenths in 1 whole and there are 60 tenths in 6 wholes.

c. 3.6 ÷ 0.1 There are ______ tenths in 3 wholes. There are ______ tenths in 6 tenths. There are ______ tenths in 3.6.

Answer: There are 30 tenths in 3 wholes. There are 6 tenths in 6 tenths. There are 36 tenths in 3.6.

Explanation: Given that 3.6 ÷ 0.1 which is 36. In that, there are 30 tenths in 3 wholes and there are 6 tenths in 6 tenths and there are 36 tenths in 3.6.

d. 12.8 ÷ 0.1 There are ______ tenths in 12 wholes. There are ______ tenths in 8 tenths. There are ______ tenths in 12.8.

Answer: There are 120 tenths in 12 wholes. There are 8 tenths in 8 tenths. There are 128 tenths in 12.8.

Explanation: Given that 12.8 ÷ 0.1 which is 128. In that, there are 120 tenths in 12 wholes and there are 8 tenths in 8 tenths and there are 128 tenths in 12.8.

e. 3 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 3 wholes.

Answer: There are 100 tenths in 1 whole. There are 300 tenths in 3 wholes.

Explanation: Given that 3 ÷ 0.1 which is 30. In that, there are 100 tenths in 1 whole and there are 300 tenths in 3 wholes.

f. 7 ÷ 0.1 There are ______ tenths in 1 whole. There are ______ tenths in 7 wholes.

Answer: There are 100 tenths in 1 whole. There are 700 tenths in 7 wholes.

Explanation: Given that 7 ÷ 0.1 which is 70. In that, there are 100 tenths in 1 whole and there are 700 tenths in 7 wholes.

g. 4.7 ÷ 0.01 There are ______ tenths in 4 wholes. There are ______ tenths in 7 tenths. There are ______ tenths in 4.7.

Answer: There are 400 tenths in 4 wholes. There are 70 tenths in 7 tenths. There are 470 tenths in 4.7.

Explanation: Given that 4.7 ÷ 0.01 which is 470. In that, there are 400 tenths in 4 wholes and there are 70 tenths in 7 tenths and there are 470 tenths in 4.7.

h. 11.3 ÷ 0.01 There are ______ tenths in 11 wholes. There are ______ tenths in 3 tenths. There are ______ tenths in 11.3.

Answer: There are 1100 tenths in 11 wholes. There are 30 tenths in 3 tenths. There are 1130 tenths in 11.3.

Explanation: Given that 11.3 ÷ 0.01 which is 1,130. In that, there are 1100 tenths in 11 wholes and there are 30 tenths in 3 tenths and there are 1130 tenths in 11.3.

Question 2. Divide. a. 2 ÷ 0.1

Answer: 2 ÷ 0.1 = 20.

Explanation: The division of 2 ÷ 0.1 is 20.

b. 23 ÷ 0.1

Answer: 23 ÷ 0.1 = 230.

Explanation: The division of 23 ÷ 0.1 is 230.

c. 5 ÷ 0.01

Answer: 5 ÷ 0.01 = 500.

Explanation: The division of 5 ÷ 0.01 is 500.

d. 7.2 ÷ 0.1

Answer: 7.2 ÷ 0.1 = 72.

Explanation: The division of 7.2 ÷ 0.1 is 72.

e. 51 ÷ 0.01

Answer: 51 ÷ 0.01 = 5,100.

Explanation: The division of 51 ÷ 0.01 is 5,100.

f. 31 ÷ 0.1

Answer: 31 ÷ 0.1 = 310.

Explanation: The division of 31 ÷ 0.1 is 310.

g. 231 ÷ 0.1

Answer: 231 ÷ 0.1 = 2,310.

Explanation: The division of 231 ÷ 0.1 is 2,310.

h. 4.37 ÷ 0.01

Answer: 4.37 ÷ 0.01 = 437.

Explanation: The division of 4.37 ÷ 0.01 is 437.

i. 24.5 ÷ 0.01

Answer: 24.5 ÷ 0.01 = 2,450.

Explanation: The division of 24.5 ÷ 0.01 is 2,450.

Question 3. Giovanna is charged $0.01 for each text message she sends. Last month, her cell phone bill included a $12.60 charge for text messages. How many text messages did Giovanna send? Answer: The number of text messages did Giovanna send is 1,260.

Explanation: Here, Giovanna is charged $0.01 for each text message she sends, and in last month, her cell phone bill included a $12.60 charge for text messages. So the number of text messages did Giovanna send is $12.60 ÷ $0.01 which is 1,260.

Question 4. Geraldine solved a problem: 68.5 ÷ 0.01 = 6,850. Ralph said, “This is wrong because a quotient can’t be greater than the whole you start with. For example, 8 ÷ 2 = 4 and 250 ÷ 5 = 50.” Who is correct? Explain your thinking. Answer: Geraldine was correct.

Explanation: Geraldine was correct. As quotient can be greater than the whole start. So Geraldine was correct.

Question 5. The price for an ounce of gold on September 23, 2013, was $1,326.40. A group of 10 friends decide to equally share the cost of 1 ounce of gold. How much money will each friend pay? Answer: Each friend pays $1326.40 ÷ 10 which is $132.64.

Explanation: Here, the price for an ounce of gold on September 23, 2013, was $1,326.40 and a group of 10 friends decide to equally share the cost of 1 ounce of gold. So each friend pays $1326.40 ÷ 10 which is $132.64.

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